This question has an answer which leads to a much more interesting "how-to" article "Ubuntu, Ruby, RVM, Rails, and You" guiding us through a fresh install of Ruby (and related things), starting from rvm. It adds insights and provides a lot of remarks for beginners -- because Ruby is truly something awful to get setup when one is without all that background knowledge and support.

The article was last updated on October 11th, 2012 and should install Ruby 1.9.3, RVM and Rails 3.2.8.

I'm posting this answer for the sake of linking the related questions.

What follows are instructions for installing Ruby on Rails(RoR) using rvm. Currently this will install ruby versions 1.9.3 and 2.0.0 with rails version 4.0.0.

Installing the latest version of RVM, Ruby and Rails (outside of the normal repositories)

Removing all currently existing ruby and rvm packages and installations.

Note: Apparently, Ubuntu has a broken version of rvm available in the repositories(No, I don't have a link to the specific issues at hand and have been unable to identify a bug in Launchpad in reference to this. There are various flame-wars regarding not using the standard repositories that I won't go into here;-)).

When one tries to run it to install an updated version of ruby through an existing rvm installation, you will be presented with a message
that redirects you to a fix located on Stack Overflow.

I quote the solution here for completeness:

Here, you will need to remove any existing ruby or rvm packages along with their
configuration files. Run the following commands from the terminal
(Ctrl-Alt-t):

During the installation download there will be some changes made to your ~/.bash_profile and other configuration files.
Please note that there are also several important instructions that appear on the screen.

It is important for you to follow them in order for your installation to be successful.
At this point, you may be prompted for your sudo/root password in order to satisfy any missing dependencies. Enter it and select [Y} at the appropriate prompt.

Note:These files are being downloaded from the stable branch on GitHub here.